In this paper we introduce a new smoothed scheme derived from the spectral Fourier method for the homogeneous Boltzmann equation recently introduced in [14, 15]. More precisely we show that using suitable smoothing filters the method can be designed in such a way that the spectral solution remains positive in time and preserves the total mass. Several numerical examples are given to illustrate the previous analysis.
On the stability of spectral methods for the homogeneous Boltzmann equation
PARESCHI, Lorenzo;
2000
Abstract
In this paper we introduce a new smoothed scheme derived from the spectral Fourier method for the homogeneous Boltzmann equation recently introduced in [14, 15]. More precisely we show that using suitable smoothing filters the method can be designed in such a way that the spectral solution remains positive in time and preserves the total mass. Several numerical examples are given to illustrate the previous analysis.File in questo prodotto:
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